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Non-Regular Statistical Estimation

  • Book
  • © 1995

Overview

Authors:
  1. Masafumi Akahira

    1. Institute of Mathematics, University of Tsukuba, Ibaraki, Japan

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    You can also search for this author in PubMed   Google Scholar

  2. Kei Takeuchi

    1. Meiji-Gakuin University, Totsukaku, Yokohama, Japan

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Statistics (LNS, volume 107)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
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  2. General Discussions on Unbiased Estimation

    • Masafumi Akahira, Kei Takeuchi
    Pages 1-19

  3. Lower Bound for the Variance of Unbiased Estimators

    • Masafumi Akahira, Kei Takeuchi
    Pages 20-60

  4. Amounts of Information and the Minimum Variance Unbiased Estimation

    • Masafumi Akahira, Kei Takeuchi
    Pages 61-83

  5. Loss of Information Associated with the Order Statistics and Related Estimators in the Case of Double Exponential Distributions

    • Masafumi Akahira, Kei Takeuchi
    Pages 84-103

  6. Estimation of a Common Parameter for Pooled Samples from the Uniform Distributions and the Double Exponential Distributions

    • Masafumi Akahira, Kei Takeuchi
    Pages 104-123

  7. Higher Order Asymptotics in Estimation for Two-Sided Weibull Type Distributions

    • Masafumi Akahira, Kei Takeuchi
    Pages 124-146

  8. “3/2-th” and Second Order Asymptotics of the Generalized Bayes Estimators for a Family of Truncated Distributions

    • Masafumi Akahira, Kei Takeuchi
    Pages 147-165

  9. Supplement The Bound for the Asymptotic Distribution of Estimators when the Maximum Order of Consistency Depends on the Parameter

    • Masafumi Akahira, Kei Takeuchi
    Pages 166-173

  10. Back Matter

    Pages 175-186
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Keywords

About this book

In order to obtain many of the classical results in the theory of statistical estimation, it is usual to impose regularity conditions on the distributions under consideration. In small sample and large sample theories of estimation there are well established sets of regularity conditions, and it is worth while to examine what may follow if any one of these regularity conditions fail to hold. "Non-regular estimation" literally means the theory of statistical estimation when some or other of the regularity conditions fail to hold. In this monograph, the authors present a systematic study of the meaning and implications of regularity conditions, and show how the relaxation of such conditions can often lead to surprising conclusions. Their emphasis is on considering small sample results and to show how pathological examples may be considered in this broader framework.

Authors and Affiliations

  • Institute of Mathematics, University of Tsukuba, Ibaraki, Japan

    Masafumi Akahira

  • Meiji-Gakuin University, Totsukaku, Yokohama, Japan

    Kei Takeuchi

Bibliographic Information

  • Book Title: Non-Regular Statistical Estimation

  • Authors: Masafumi Akahira, Kei Takeuchi

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-2554-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1995

  • Softcover ISBN: 978-0-387-94578-1Published: 18 August 1995

  • eBook ISBN: 978-1-4612-2554-6Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VIII, 188

  • Topics: Applications of Mathematics

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